I bought the steam version of final fantasy 14 realm reborn and made a account on it.
Now my question is if I buy the normal (non steam) version of final fantasy 14 will I be able to log in with my ff14 steam account or do I have to make a new account.
If you bought the regular game (NOT: Heavensward), so you can play independently of Steam, yes, you should be fine.
If you try to use a PC Heavensward Expansion (not bought from Steam) with a Steam-FFXIV-base game, it will fail.
Unfortunately no, if you bought the steam version of the base game you'll have to order the expansion through steam too.